Our group recently showed that the Seidel primary ray aberration coefficients of an axis-symmetrical system can be accurately determined using the third-order Taylor series expansion of a skew ray R¯m on an image plane. This finding inspires us to determine the third-order derivative matrix of R¯m with respect to the vector X¯0 of the source ray, i.e., ∂R¯ 3m/∂X¯ 30, under reflection/refraction at a flat boundary. Finite difference methods using the second-order derivative matrix, ∂R¯ 2m/∂X¯ 20, require multiple rays to compute ∂R¯ 3m/∂X¯ 30 and suffer from cumulative rounding and truncation errors. By contrast, the present method is based on differential geometry. Thus, it provides a greater inherent accuracy and requires the tracing of just one ray. The proposed method facilitates the analytical investigation of the primary aberrations of an axis-symmetrical system and can be easily extended to determine the higher-order derivative matrices required to explore higher-order ray aberration coefficients.
|頁（從 - 到）||1435-1441|
|期刊||Journal of the Optical Society of America A: Optics and Image Science, and Vision|
|出版狀態||Published - 2019 九月|
All Science Journal Classification (ASJC) codes